Charge Balance Equations Research Articles

Analytical model for flexoelectric sensing of structural response considering bonding compliance

Flexoelectricity has generated huge interest as an alternative to piezoelectricity for developing electromechanical systems such as actuators, sensors, and energy harvesters. This article presents a generic theoretical framework for the sensing mechanism of a flexoelectric sensor bonded to a host beam through an adhesive layer. The model incorporates piezoelectric and flexoelectric effects and considers both shear-lag and peel stresses at the sensor-beam interface. The formulation also includes the electric field gradient terms that are often overlooked. Consistent one-dimensional constitutive relations and governing equations of equilibrium are derived from the electric Gibb’s energy density function and extended Hamilton’s principle. The sensor is assumed to follow the Euler–Bernoulli beam-type membrane and bending deformation behaviour. Closed-form solutions are obtained for the interfacial stresses by analytically solving a seventh-order non-homogeneous ordinary differential equation, satisfying the stress-free boundary conditions at the sensor edges. The induced electric potential at the sensor top is derived by solving a fourth-order differential equation obtained from the charge balance equation, satisfying the electric boundary conditions. For validation, the sensor output is compared with the results of the existing non-rigid bonding piezoelectric sensor model. Numerical results show a significant impact of non-rigid bonding and the electric field gradient terms on the induced electric potential. Further, the importance of bonding compliance on the interfacial stress distributions is illustrated. Finally, the effects of adhesive and transducer thicknesses on the peak amplitudes of interfacial stresses and sensory potential are presented.

A Unified Equation Derived from the Charge Balance Equation for Constructing Acid-Base Titration Curve and Calculating Endpoint Error

A Unified Equation Derived from the Charge Balance Equation for Constructing Acid-Base Titration Curve and Calculating Endpoint Error

The role of the solving strategy in electrokinetic transport modelling in saturated porous media

The characterisation of the reactive transport of solutes is a complex problem that is applied in many fields of industry and environmental management. However, this problem has been treated with multiple mathematical approaches. This paper reviews several strategies for solving the different physical constraints that must be applied to this type of problem using COMSOL Multiphysics. The number of mass balance equations of the chemical species is evaluated together with the use of Gauss’s Law or electric charge balance to analyse the no-charge accumulation or electroneutrality conditions as electrical constraints. Problems of natural diffusion and electrokinetic transport in saturated porous materials are evaluated for electroconductive and nonconductive solid matrices in both potentiostatic and galvanostatic operation modes. Of all the solving strategies proposed, only one is valid and consistent for all types of problems presented. This approach is based on posing a mass balance equation of less (N-1) than the species in solution (N), solving for the mass of the missing species by electroneutrality and imposing the condition of no electric charge accumulation on the charge balance equation.

Investigating the effect of blending of diamine and alkanolamine for CO2 capture: Experiment and thermodynamic modeling of CO2-AEEA-DEA-H2O system

This study reports the experimental data on CO2 solubility in aqueous aminoethylethanolamine (AEEA) and diethanolamine (DEA) under different amine blending ratios (9:21, 15:15 and 21:9 wt% AEEA: DEA, respectively and remaining 70 wt% being the water), CO2 partial pressure up to 477.4 kPa and temperatures up to 393.15 K. The complex nature of AEEA diamine and DEA was thermodynamically modeled to evaluate the behavior of aqueous blend of AEEA and DEA for CO2 capture. The electrolyte nonrandom two liquid (electrolyte NRTL) activity coefficient model is used to incorporate the nonideality of the system. The system of blended aqueous AEEA and DEA contained twelve equilibrium equations, three mass balance equations, one charge balance equation and one hydronium ion-based polynomial. These equations were simultaneously solved by using an inhouse built MATLAB code to determine the CO2 loading, CO2 cyclic capacity, pH, heat of absorption, activity coefficients and concentration of seventeen species in the system. Model results have been compared with literature and inhouse experimental data, which are in a good agreement. Furthermore, study reports activity coefficients, mole fractions of seventeen species, dependence of CO2 loading on temperature, pressure and concentration of individual amine. The Absolute average deviation percent in the model and experimental data for AEEA, DEA and their blend are 9.90%, 7.61% and 8.55%, respectively for CO2 loading.

Research on battery charging automatic equalization system based on double closed loop controller

In order to improve the equalization control efficiency of the battery charge equalization system, this paper applies the double closed-loop controller to the battery charge automatic equalization system. First, the overall block diagram of the hardware circuit of the charging system is designed, and the switching control of charging and discharging is completed by using TMS320F2812 chip. Secondly, the optimal charging current is calculated according to Mars law. Then, a double closed-loop controller is introduced to balance the battery charge, and the charge balance equation is constructed and solved. Finally, the adjusted parameters are obtained to realize the automatic charging equalization control. The experimental results show that the equalization control time of this method is always within 25s, which indicates that its charge equalization control effect is good.

Pattern formation on dynamic membranes.

Pattern formation defines cell identities and plays a crucial role in arguably all membrane functionality such are cell division, motility, communication, adhesion, etc. Cell often evolves by changing their shape, which translates to membrane dynamics, hence leading to pattern formation on dynamic surfaces. While pattern formation on static shapes has been intensively studied both theoretically and experimentally, the understanding of patterning on moving shapes remains largely elusive. We study force distribution on dynamic but initially spherical or cylindrical shapes by our surface dynamics equations. For simplicity, we consider small deformation of incompressible sphere and cylinder and show that shape dynamics induce nonuniform force distributions, therefore clarifying spontaneous polarisation, symmetry breaking, and rich static and moving pattern formations. Based on surface dynamics equations we derive a generic Young-Laplace equation which indicates that practically any static and dynamic patterns are possible in incompressible systems and if so, the question is what is the underlying mechanism that controls cell identity? The answer to the problem is again a surface dynamics equation that guarantees mass conservation. In other words, dynamic surfaces induce dynamic surface mass density that is governed by a generic mass balance equation and the last one controls the identity. While mass balance itself is regulated by an active or passive influx of material particles on the surface. The last statement for cell membrane means that membrane mass balance is in full correlation with cell-governed reaction, synthesis, and diffusion. The same statement can be reached for the charge balance equation which is also part of surface dynamics equations.

Thermodynamic modeling and parameter estimability analysis of a wet phosphoric acid process with impurities

In this work, a thermodynamic-based model of an industrial phosphoric acid process is developed. It consists of mass and charge balance equations along with equilibria and Pitzer’s model equations. The latter involves several unknown parameters to be identified from experiments. Experimental measurements consisting mainly of speciation data of sulfur and phosphate-based systems, solubility data of ten minerals, and water activity of eight binary systems, are used. Part of the measurements are collected from the literature and the rest is carried out in the laboratory. A global estimability analysis method recently developed allowed us to determine which parameters can be identified from the available measurements, and those to be fixed from the literature or from previous works. The Pearson product moment coefficient is computed and found to be higher than 97% for all the identification cases, demonstrating the accuracy of the model. The resulting model is then validated by means of additional measurements which are not used for its identification, using the t-Student, Fisher–Snedecor and Kolmogorov–Smirnov tests. Normalized root mean square errors are computed for all the validation cases and found to be less than 7%, showing good model performance. The validated model can now be used to predict several properties needed for the simulation and optimization of the industrial process under study.

Synthesis of PWM Converters From Conversion Ratios Using Flux- or Charge-Balance Equations

To cater to the heterogeneity in emerging applications, researchers have constantly been driven to invent novel dc–dc converter topologies. A review of prior art in dc–dc converter synthesis methods shows that many converter choices are available for a given input and output specification. This article quantifies the number of these choices using the flux balance equation (FBE). As the number of state variables that can be used to derive the FBE is limited, it is possible to find out the total number of possible FBEs available for a given voltage conversion ratio. Once the FBEs are known, synthesizing a converter is carried out as an inverse problem. Three different strategies to solve this inverse problem of converter synthesis and some critical synthesis results are summarized in this article. The dual synthesis of current-fed topologies with given current conversion ratios based on the charge balance equation (CBE) is also demonstrated. Four novel topologies were synthesized to illustrate the effectiveness of the CBE-based synthesis method. The mathematical formulation of the CBE-based inverse problem and the quantification of complexities in solving it are also reported.

Impact of unpreventable induced interface trapped charges on HZO based FDSOI NCFET

In this paper, the effect of oxide-semiconductor interface trapped charges on the performance of 22-nm Fully Depleted Silicon on Insulator (FDSOI) Negative Capacitance FET (NCFET) has been systematically investigated. Metal-Ferroelectric-Metal-Insulator-Semiconductor (MFMIS) type NCFET with zirconium doped HfO2 (HZO) as the ferroelectric material is considered for this work. The simulation of the underlying Metal-Insulator-Semiconductor (MIS) structure has been carried out in a well-calibrated TCAD environment to extract the gate charge. Which is subsequently used to solve 1D Landau-Khalatnikov (1D-LK) model to find the voltage across ferroelectric capacitor. The presence of trap charges is unavoidable in modern devices, which affects the charge balance equation as well as the performance & reliability of the device. NCFET being one of the potential candidates to be adopted by industry for ultra-low power applications in the future according to the International Roadmap for Devices and Systems (IRDS), investigation of trap charges becomes crucial. Due to its multilayer stacking, the transfer characteristics are analyzed for various ferroelectric thicknesses with exhibition of an intersection point, which is demonstrated for the first time. Simulation of variation of device performance metrics like minimum sub-threshold swing (min. SS), transconductance (gm), off-state drain current (Ioff) & amplification factor (AV) are analyzed and compared for various interface trapped charge densities. It is predicted that the device performance either enhances or degrade depending on the type of trapped charges present.

Charging of radioactive and environmental airborne particles

The charging of various airborne particles was investigated using single-particle levitation and charge-balance equations. Though radioactive decay and triboelectrification can induce charging, it is typically assumed that the aerosols in a radioactive plume will not carry significant charge at steady state since atmospheric particles can have their charge neutralized through the capture of adjacent counter-ions (i.e., diffusion charging). To assess this assumption, we directly measured the surface charge and charge density of various triboelectrically charged aerosols including radioactive uranium oxide (<1 μm), urban dust, Arizona desert dust, hydrophilic and hydrophobic silica nanoparticles, and graphene oxide powders using an electric field-assisted particle levitator in air. Of these particles, uranium oxide aerosols exhibited the highest surface charge density. Charge balance equations were employed to predict the average charge gained from radioactive decay as a function of time and to evaluate the effects of diffusion charging on triboelectrically charged radioactive and non-radioactive particles in the atmosphere. Simulation results show that particles, initially charged through triboelectrification, can be quickly discharged by diffusion charging in the absence of radioactive decay. Nevertheless, simulation results also indicate that particles can be strongly charged when they carry radionuclides. These experimental and simulation results suggest that radioactive decay can induce strong particle charging that may potentially affect atmospheric transport of airborne radionuclides.

A 2D Modelling Approach for Predicting the Response of a Two-Chamber Microbial Fuel Cell to Substrate Concentration and Electrolyte Conductivity Changes

Bioelectrochemical systems have been the focus of extensive research due to their unique advantages of converting the chemical energy stored in waste to electricity. To acquire a better understanding and optimize these systems, modelling has been employed. A 2D microbial fuel cell (MFC) model was developed using the finite element software Comsol Multiphysics® (version 5.2), simulating a two-chamber MFC operating in batch mode. By solving mass and charge balance equations along with Monod–Butler–Volmer kinetics, the operation of the MFC was simulated. The model accurately describes voltage output and substrate consumption in the MFC. The computational results were compared with experimental data, thus validating the model. The voltage output and substrate consumption originating from the model were in agreement with the experimental data for two different cases (100 Ω, 1000 Ω external resistances). A polarization curve was extracted from the model by shifting the external resistance gradually, calculating a similar maximum power (47 mW/m2) to the observed experimental one (49 mW/m2). The validated model was used to predict the MFC response to varying initial substrate concentrations (0.125–4 g COD/L) and electrolyte conductivity (0.04–100 S/m) in order to determine the optimum operating conditions.

Extraction of Interface-Trap Densities of the Stacked Bonding Structure in 3D Integration Using High-Frequency Capacitance-Voltage Technique.

An extraction method of the interface-trap densities (Dit) of the stacked bonding structure in 3D integration using high-frequency capacitance–voltage technique is proposed. First, an accurate high-frequency capacitance–voltage model is derived. Next, by numerically solving the charge-balance equation and charge conservation equation, Dit is extracted by fitting the measured and calculated capacitance–voltage curves based on the derived model. Subsequently, the accuracy of the derived model is verified by the agreements between the analytical results and TCAD simulation results. The average extraction error proves the precision and efficiency of the extraction method. Finally, the stacked bonding structure has been fabricated, and Dit at the interface between silicon and insulator is extracted to diagnose and calibrate the fabrication processes.

Experimental and thermodynamic modeling of CO2 absorption into aqueous DEA and DEA+Pz blended solutions

The important environmental concern of the carbon dioxide (CO2) capture by the absorption process with amine solutions is studied in the current study. The experiments are performed at operating conditions of a temperature range of 25 65 °C, a pressure range of 1.5 6.5 bar, diethanolamine (DEA) concentration of 0 1.5 M, PZ concentration of 0 0.5 M, and stirrer speed of 0 300 rpm. The effects of operating conditions on CO2 loading, absorption rate, and mass transfer flux are investigated into two solutions of DEA and DEA+piperazine (Pz) blend in a stirred reactor. In the DEA+CO2+H2O system, by increasing stirrer speed from 0 to 300 rpm, the maximum values of CO2 loading and mass transfer flux at the same DEA concentration are increased 65% and 137%, respectively. The CO2 loading and mass transfer flux have higher values at higher initial pressures. The predicted values for species concentrations into the DEA+CO2+H2O system are also evaluated based on the Pitzer model, mass, and charge balance equations. The results showed that by increasing stirrer speed, the concentration of DEA molecule is decreased 40% but the concentrations of other ions and molecules are increased. In the DEA+Pz+CO2+H2O system, the results indicated that adding Pz to the absorbent solution was more efficient in CO2 capture relative to only the DEA solution. The equilibrium CO2 loading is increased by 20% and 16% for blend solutions with 4:6 and 6:4 molar ratios of DEA and Pz, respectively, but using only Pz solution is increased it up to 29%.

CO2 absorption mechanism in aqueous ternary solutions of alkanolamines: Experimental and thermodynamic modeling approaches

The absorption mechanism of CO2 in an aqueous solution containing three alkanolamines was analyzed experimentally and theoretically. The vapor–liquid equilibrium of a CO2–monoethanolamine (MEA)–diisopropanolamine (DIPA)–2-amino-2-methyl-propanol (AMP)–H2O system was evaluated experimentally over a wide temperature range (323.15–393.15 K) at several MEA:DIPA:AMP:H2O blending ratios (15:10:5:70, 10:10:10:70, 7.5:7.5:15:70, and 5:15:10:70 wt%). The successive substitution method was used to calculate the concentrations of five molecules (CO2, MEA, DIPA, AMP, and H2O) and nine electrolytes (four cations and five anions) in the liquid phase by solving eight equilibrium equations, four mass balance equations, and one charge balance equation. The Deshmukh–Mather model, which is based on an activity coefficient approach, and the fugacity coefficient model were used to evaluate the nonideality of the liquid and vapor phases, respectively. Thereafter, the effect of the MEA:DIPA:AMP blending ratio was evaluated using the triangular diagrams of the carbamate, bicarbonate and carbonate molar fractions in liquid phase, CO2 loading ratio, CO2 cyclic capacity, and heat of CO2 absorption.

Compact Modeling and Analysis of Charge and Device Capacitance for SELBOX Junctionless Transistor

A charge based compact drain current and capacitance modeling has been developed to describe the transfer and Capacitance-Voltage characteristics of the proposed device. The inversion charge density of the proposed model is defined on the basis of the surface potential model equation at the source and the drain end. These inversion charges are evaluated by the Ward Dutton partition method using the current continuity principle and charge balance equations. Using these inversion charges, a drain current model is discussed for the proposed device, which is based on implicit unified charge control expression. This model defined all the possible intrinsic capacitances analytically derived by the terminal charges associated with the terminal voltages. This compact model is valid in the weak, moderate and strong regime of the device operation. The transfer characteristics of the drain current and C-V characteristic of capacitances have been validated using 2-D numerical simulation.

Tanks-in-series model for high-temperature electrochemical hydrogen pump

A tanks-in-series model has been developed for modeling the transfer processes in a high-temperature proton exchange membrane electrochemical hydrogen pump (HT-EHP). The model is based on the mass and charge balance equations. The predicted HT-EHP performance is consistent with experimental literature data.

Kinetic Study on the Si&lt;sub&gt;3&lt;/sub&gt;N&lt;sub&gt;4&lt;/sub&gt; Etching in Superheated Water

Wet etching of Si3N4 was conducted in superheated water at 160 °C with different additives type and concentration. In general, etching rate of Si3N4 increased with the pH of solution. However, it is difficult to fully explain the Si3N4 etching behavior just with the pH of solution. The OH- concentration (or pH) in superheated water at 160 °C are different from the pH of solution at room temperature. Therefore, the OH- concentrations in superheated water at 160 °C were calculated using van't Hoff equation, equilibrium constant equations, mass and charge balance equations. The calculated OH- concentration at 160 °C showed better correlation with Si3N4 etching rate than that of initial pH of solution.

Effect of Blending Ratio and Temperature on CO2 Solubility in Blended Aqueous Solution of Monoethanolamine and 2-Amino-2-methyl-propanol: Experimental and Modeling Study Using the Electrolyte Nonrandom Two-Liquid Model.

This paper reports the newly measured experimental data for CO2 solubility in a blended aqueous solution of monoethanolamine (MEA) and 2-amino-2-methyl-propanol (AMP) at different amine mixing ratios (MEA/AMP/H2O = 9:21:70, 15:15:70, and 21:9:70 wt %) and working temperatures (323.15, 373.15, and 383.15 K). The successive substitution method was used for calculating the mole fractions of all molecules (four molecules) and electrolytes (three cations and four anions) from the equilibrium along with the material and charge balance equations (11 equations). The electrolyte nonrandom two-liquid (e-NRTL) model was used to investigate nonideality in the liquid phase. Using the abovementioned thermodynamic models, the partial pressures of CO2 in the gas phase, mole fractions of all components in the liquid phase, pH variations, heats of absorption, and cyclic capacities of CO2 according to the absorption/desorption temperature and the blending ratio of MEA/AMP were estimated.

Methodology for Determining Point of Zero Salt Effect of Clays in Terms of Surface Charge Properties

Surface charge properties of colloids can be studied from their point of zero charge (PZC) measurements. The point of zero salt effect (PZSE), a category of PZC, indicates the pH value at which the effect of electrolyte concentration on a pH-dependent charge is zero. In the present study, it was mathematically deduced that for clay minerals, the rate change of pH and zeta potential with ionic concentration approaches zero at a pH value corresponding to the PZSE of the soil. The procedure is based on applying the constraint of electroneutrality to the charge-balance equation for colloids in equilibrium with an electrolyte. The theoretical observations were corroborated experimentally by obtaining the pH and zeta potential variations of three mineralogically diverse soils and comparing the values with the standard salt titration results. The study identifies PZSE from pH measurement as a more suitable approach for soil exhibiting variable charge. In the case of highly reactive soils, PZSE measurement using a divalent electrolyte medium yielded comparable results. In view of the obtained results, the proposed method can be an alternative for PZSE determination of clay minerals.

Analytical Model of a Surface Barrier Discharge Development

The propagation of the front of a single surface dielectric barrier microdischarge is studied using an analytical model based on the charge balance equation. The model allows one to find analytical dependences of the discharge propagation velocity and the length of the discharge zone on the parameters of the dielectric barrier and applied voltage pulse. To solve the problem, the results of numerical simulations of the distributions of the electric field, potential, and electron density along the discharge channel are used. The results obtained with the help of the proposed model agree qualitatively with available experimental data.